Download Designing Clinical Trials for Testing Overall Survival in the Presence

Objective
Methods
Results
Discussion
Designing Clinical Trials for Testing Overall Survival
in the Presence of Crossover at Progression
Fang Xia, Stephen L. George
Duke University
May, 2014
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Objective
To present a design tool to assess the power for OS in the
presence of treatment switching or crossover after progression
from the control treatment to the experimental treatment
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Multi-state Model
Figure 1 : A simple multi-state model.
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Multi-state Model
Notation from Fleisher et al (2009)
TTP: time to progression
X : time to death without progression
OS 0 : time until death after progression (also noted as SPP)
PFS =⇢min(TTP, X )
TTP + OS 0
OS =
PFS
if TTP < X
otherwise
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Multi-state Model with Crossover
p: the probability of crossover for control patients
C
3 (t): the hazard function for non-crossover control patients
C
4 (t): the hazard function for control patients who crossover
Figure 2 : Multi-state model for control arm with crossover to
experimental treatment after progression.
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Relationship between PFS and OS
Assumption
The time in each state is exponentially distributed
TTP, X and OS’ are independent
Then
PFS = min{TTP, X } ⇠ Exp( 1 + 2 )
Probability of death before progression: ! =
2
1+ 2
The distribution function of OS can be derived by extending
the results of Fleisher et al (2009) to the case of crossovers
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Design Parameter Required
Logrank tests are used to compare the treatments
Table 1 : Items to be Specified in the Design
↵1
↵2
1
1
1
2
Nmax
Tmax
a
MPFS
MOS 0
!
p
Type I error rate for PFS
Type I error rate for OS
Power for PFS
Power for OS
Maximum feasible sample size
Maximum study duration
Accural rate
Median PFS
Median OS’ (control-no crossover/crossover; experimental)
Probability of death before progression
Probability of crossover (control)
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Required Number of Events and Duration of Study for PFS
E + E
4(Z↵1 /2 + Z 1 )2
E
1
2
,
where
=
=
2
C
C
(ln )
C
1 + 2
The expected time to achieve DPFS events can be derived as in
George and Desu (1974) by solving the following equation for t
DPFS =
DPFS
at ⇤
=
[(1
2
exp
t
C t(exp C
Ct
⇤
⇤
)
) + (1
exp
t
E t(exp E
Et
⇤
⇤
)
)]
where t ⇤ is the minimum of t and the accural time T.
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Required Number of Events and Duration of Study for OS
The situation for OS is more complicated because the hazard
functions and hazard ratios are not constant
Want to determine the required OS events DOS and the
optimal sample size N ⇤
N ⇤ : the smallest sample size N that achieves the appropriate
statistical power for OS within the maximum allowable
expected study duration Tmax
Nmin : 1.25 ⇤ DPFS
Nmax : the pre-specified maximum sample size allowed
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Required Number of Events and Duration of Study for OS
Figure 3 : Tree diagram for determining the optimal sample size.
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Simulation Example: Hazard Ratios for OS
Figure 4 : Hazard Ratios for OS
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Discussion
We present a design tool to assess the power for testing OS in
the presence of treatment switching or crossover after
progression from the control treatment to the experimental
treatment
The approach taken here enables one to assess the power for
testing OS under various realistic scenarios and to check the
sensitivity of the power to changes in the assumed model
parameters in the model
Possible to further develop the process to include prognostic
factors, loss to follow up, time-varying intensity functions for
the multi-state model etc.
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References
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of Cancer Drugs and Biologics 2007.
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3. Ghimire S, Kyung E and Kim E. Reporting Trends of Outcome Measures in Phase II and Phase III
Trials Conducted in Advanced-Stage Non-small-cell Lung Cancer. Lung. 2013; 191: 313-9.
4. Carroll KJ. Analysis of progression-free survival in oncology trials: some common statistical issues.
Pharm Stat. 2007; 6: 99-113.
5. Fleming TR, Rothmann MD and Lu HL. Issues in using progression-free survival when evaluating
oncology products. J Clin Oncol. 2009; 27: 2874-80.
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effect of assessment schedule on progression-free survival. J Natl Cancer Inst. 2007; 99: 428-32.
7. Hougaard P. Multi-state Models: A Review. Lifetime Data Anal. 1999; 5: 239-64.
8. Fleischer F, Gaschler-Markefski B and Bluhmki E. A statistical model for the dependence between
progression-free survival and overall survival. Statistics in Medicine. 2009; 28: 2669-86.
9. Broglio KR and Berry DA. Detecting an Overall Survival Benefit that Is Derived From
Progression-Free Survival. J Natl Cancer Inst. 2009; 101: 1642-9.
10. Redman MW, Goldman BH, LeBlanc M, Schott A and Baker LH. Modeling the Relationship
between Progression-Free Survival and Overall Survival: The Phase II/III Trial. Clin Cancer Res. 2013;
19: 2646-56.
11. Zhang LJ, Ko CW, Tang SH and Sridhara R. Relationship Between Progression-Free Survival and
Overall Survival Benefit: A Simulation Study. Ther Innov Regul Sci. 2013; 47: 95-100.
12. George SL and Desu MM. Planning the size and duration of a clinical trial studying the time to
some critical event. J Chronic Dis. 1974; 27: 15-24.
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Thank you.
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